What is the area of a triangle that has two sides that each have a len

Question

What is the area of a triangle that has two sides that each have a length of 10, and whose perimeter is equal to that of a square whose area is 81?

A. 30

B. 36

C. 42

D. 48

E. 60

rajatchopra1994 · Answer

Explanation:

Side of Square = (side)^2 = 81 
side = 9
Perimter = 36
So, 3rd side of Triangle i.e Base= 36-20 = 16
So, height of isosceles Triangle= h^2 = 10^2 - 8^2
P = 6

Area of Triangle = 1/2xbxh = 1/2 x 16 x 6
Area = 48

IMO-D

Akp880 · Answer

What is the area of a triangle that has two sides that each have a length of 10, and whose perimeter is equal to that of a square whose area is 81?

A. 30

B. 36

C. 42

D. 48

E. 60

Explanation:

are of square=81 means side length=9
perimeter of triangle=perimeter of square=4*9=36

given two sides of triangle are of 10 unit length then 
perimeter of triangle=10+10+third side=36
 third side length=16 units

Now in isosceles triangle(two sides equal given) altitude^2= (any of equal side)^2- (1/2 base length)^2
altitude^2=10^2-8^2
=6^2
 altitude=6 units

Henc  area=1/2*base *altitude 
=(1/2)*16*6
= 48

Hence D is the correct answer.

ScottTargetTestPrep · Answer

Solution:
 
Since the square has an area of 81, it has a side length of √81 = 9 and hence, its perimeter is 9 x 4 = 36. Since the triangle has the same perimeter, its perimeter is 36 and hence, the third side of the triangle is 36 - 10 - 10 = 16. Since the 3 sides of the triangle are 10, 10, and 16, the triangle is an isosceles triangle with base of 16. If we draw the height from the vertex of the triangle to the base, the height divides the isosceles triangle into two congruent right triangles with a leg = 16/2 = 8 and the hypotenuse = 10. Each of these triangles must then be a 6-8-10 right triangle with 6 being the height of the isosceles triangle. Therefore, the area of the isosceles triangle is ½ x 16 x 6 = 48.

Answer: D

MathRevolution · Answer

Area of square:  (side)^2  = 81 and hence side = 9

Perimeter of square: 4 * side = 4 * 9 = 36

=> Triangle perimeter is equal to 36 and it has two sides equal to 10.

=> 10 + 10 + Third side : 36

=> Base: 16

Dropping a height in the center of the triangle will result in two right-angle triangles with hypotenuse (10) and base ( \frac{16}{2}  = 8).

=>  (Height)^2 = (10)^2 - (8)^2

=>  (Height)^2  = (100 - 64) = 36

=> Height = 6

=> Area of triangle:  \frac{1}{2}  * b * h =  \frac{1}{2}  * 16 * 6 = 48

Answer D

What is the area of a triangle that has two sides that each have a len

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What is the area of a triangle that has two sides that each have a len

Prep Toolkit

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