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The answer is 4.5 cm, 6.0 cm and 7.5 cm.

This browser has stopped supporting superscripts so I will use sq for squared numbers and sqrt for square roots.

Suppose the three sides are x y and z cm, that the base is x and the other leg is y so that the hypotenuse is z.

Perimeter = 4*x => x+y+z = 4x and therefore y+z = 3x .. .. .. .. (1)

Next, Area = 13.5 sq cm => 0.5*x*y = 13.5,

=> x*y = 27 or y = 27/x and so, substituting for y in (1) gives 27/x + z = 3x

and therefore, z = 3x - 27/x

so that sq(z) = 9*sq(x) - 162 + sq(27/x) .. .. .. .. .. .. .. .. .. .. (2)

Finally, by Pythagoras sq(x) + sq(y) = sq(z)

=> sq(x) + sq(27/x) = sq(z) .. .. .. .. .. .. .. .. .. .. .. .. (3)

Equating (2) and (3)

9*sq(x) - 162 + sq(27/x) = sq(x) + sq(27/x)

=> 8*sq(x) = 162 => sq(x) = 162/8 = 20.25

=> x = sqrt(20.25) = 4.5

Then y = 27/x = 27/4.5 = 6.0

and z = 3x - 27/x = 13.5 - 6 = 7.5

Q: What are the dimensions of a right angle triangle when its perimeter is 4 times its base with an area of 13.5 square cm showing all aspects of work?

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Divide the perimeter by 2 then find two numbers that have a sum of 9.9 and a product of 24.3 which will work out as 5.4 and 4.5 by using the quadratic equation formula. Check: 2*(5.4+4.5) = 19.8 cm which is the perimeter Check: 5.4*4.5 = 24.3 square cm which is the area Therefore the dimensions of the rectangle are: 5.4 cm and 4.5 cm

Such a triangle would be impossible to construct with the given 3 dimensions because in order to construct a triangle the sum of its 2 shortest sides must be greater than the length of its longest side.

These are basically the steps: * Use the formula for the area of a triangle to calculate the height. * Use the height and half the base to calculate the lateral sides. Use the Pythagorean Theorem. (It helps to draw a sketch, to visualize the situation.) * Add the three sides to get the perimeter.

First find its height by dividing its area and use Pythagoras to find its sides: Height: 84.9072/(0.5*15.96) = 10.64 cm Half its base: 7.98 cm Pythagoras: 10.64 squared plus 7.98 squared = 176.89 and its sq rt = 13.3 Perimeter therefore is: 2*(13.3)+15.96 = 42.56 cm

Let the dimensions be x and x+3 Perimeter: 4x+6 Area: x(x+3) = 2(4x+6) => x^2 +3x = 8x+12 => x^2 -5x-12 = 0 Solving the above quadratic equation: x has a positive value of 6.77 rounded to 2dp Therefore dimensions are: 6.77 cm and 9.77 cm

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Divide the perimeter by 2 then find two numbers that have a sum of 9.9 and a product of 24.3 which will work out as 5.4 and 4.5 by using the quadratic equation formula. Check: 2*(5.4+4.5) = 19.8 cm which is the perimeter Check: 5.4*4.5 = 24.3 square cm which is the area Therefore the dimensions of the rectangle are: 5.4 cm and 4.5 cm

Such a triangle would be impossible to construct with the given 3 dimensions because in order to construct a triangle the sum of its 2 shortest sides must be greater than the length of its longest side.

These are basically the steps: * Use the formula for the area of a triangle to calculate the height. * Use the height and half the base to calculate the lateral sides. Use the Pythagorean Theorem. (It helps to draw a sketch, to visualize the situation.) * Add the three sides to get the perimeter.

First find its height by dividing its area and use Pythagoras to find its sides: Height: 84.9072/(0.5*15.96) = 10.64 cm Half its base: 7.98 cm Pythagoras: 10.64 squared plus 7.98 squared = 176.89 and its sq rt = 13.3 Perimeter therefore is: 2*(13.3)+15.96 = 42.56 cm

Let the dimensions be x and x+3 Perimeter: 4x+6 Area: x(x+3) = 2(4x+6) => x^2 +3x = 8x+12 => x^2 -5x-12 = 0 Solving the above quadratic equation: x has a positive value of 6.77 rounded to 2dp Therefore dimensions are: 6.77 cm and 9.77 cm

Let the sides be s:- If: 0.5*s squared*sin(60 degrees) = 97.428 Then: s = square root of 97.428*2/sin(60 degrees) => 15.00001094 Perimeter: 3*15 = 45 cm

I suggest that you do the following:* Convert the meters to centimeters, to have compatible units.* Write the equation for the area of the rectangle. Replace the variable "a" (area) with the known area.* Write the equation for the perimeter of a rectangle. Replace the variable for the perimeter with the known perimeter (in cm).* Use any method to solve the simultaneous equations.Another Answer:-Let the dimensions be x and yIf: 2x+2y = 100 then x+y = 50 and x = 50-yIf: xy = 600 then (50-y)y = 600 and so 50y-y2-600 = 0Solving the quadratic equation: y = 20 or y = 30Therefore by substitution the dimensions are: when y = 20 cm then x = 30 cm

It must be an equilateral triangle if it's a regular shape and so:- If: 0.5*side2*sin(60) = 16*square root of 3 Then: its sides are 8 cm by making 'side' the subject of the above equation

it should be a triangle with no red showing

Here are the key aspects of work; I'll leave the details of the calculation to you. 1) Write an equation for the area, in terms of variables "w" and "h" (for width and height). 2) Write an equation for the length of the diagonal, in terms of "w" and "h". (Hint: Use the Pythagorean Theorem.) 3) Solve the two equations. 4) Calculate the perimeter, based on length and width.

Perimeter = 29 cm so each side is 7.25 cm. The triangle formed by the diagonal and two sides has sides of 7.25, 7.25 and 11.8 cm so, using Heron's formula, its area is 24.9 square cm. Therefore, the area of the rhombus is twice that = 49.7 square cm.

Let the number be x and so: 2x squared+3x = 77.2502 Then: 2x squared+3x-77.2502 = 0 Solving the above quadratic equation gives x a positive value of 5.51 Thus: congruent sides are each 30.3601 cm and base is 16.53 cm Check: 30,3601+30.3601+16.53 = 77.2502 cm