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Musya8 [376]
3 years ago
12

A rectangle is inscribed in a right isosceles triangle, such that two of its vertices lie on the hypotenuse, and two other on th

e legs. What are the lengths of the sides of the rectangle, if their ratio is 5:2, and the length of the hypotenuse is 45 in? (Two cases)
CASE 1: (Blank) (blank) (Blank) (blank)
CASE 2: (Blank) (blank) (Blank) (blank)

Mathematics
1 answer:
Rufina [12.5K]3 years ago
3 0

Answer:

Part 1) The base is 25\ in  and the height is 10\ in

Part 2) The base is 7.5\ in  and the height is 18.75\ in

Step-by-step explanation:

case 1) Right isosceles triangle of the left

Let

x------> the base of the rectangle

y----> the height of the rectangle

Remember that

In a right isosceles triangle the lengths of the legs of the triangle is the same

y+x+y=45

2y+x=45 ----> equation A

\frac{x}{y} =\frac{5}{2}

x=2.5y -----> equation B

substitute equation B in the equation A

2y+2.5y=45

4.5y=45

y=10\ in

Find the value of x

x=2.5(10)=25\ in

case 2) Right isosceles triangle of the right

Let

x------> the base of the rectangle

y----> the height of the rectangle

Remember that

In a right isosceles triangle the lengths of the legs of the triangle is the same

y+x+y=45

2y+x=45 ----> equation A

\frac{y}{x} =\frac{5}{2}

y=2.5x -----> equation B

substitute equation B in the equation A

2(2.5x)+x=45

6x=45

x=7.5\ in

Find the value of y

y=2.5(7.5)=18.75\ in

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