Question

Steve made a sign for his room that is shaped like a triangle. It is 4.5 feet long and 3 feet high. He wants to make another sign that is shaped like a triangle and similar to the first sign. The new sign will be 4 feet high.

Part A

Write a proportion that Steve can use to find the length, x, of the new sign.

Part B

What is the length, in feet, of the new sign? Make sure to show your work and explain your reasoning.

Answer 1

Answer: PART A :
`(4.4)/(x)` =
`(3)/(4)`

PART B : 5.9 FEET

Explanation:

Length of the first sign = 4.4 feet

height of the first sign = 3 feet

Length of the second sign = x feet

height of the second sign = 4 feet

If two shapes are similar , then the ratio of their sides are equal,

That is ;

`(h_(1))/(h_(2) )` =
`(L_(1))/(L_(2) )`

PART A

`(4.4)/(x)` =
`(3)/(4)`

PART B

`(4.4)/(x)` =
`(3)/(4)`

cross multiplying , we have

3x = 4.4 x 4

3x = 17.6

Divide through by 3

x = 17.6/3

x = 5.86666666666667

x≈ 5.9 feet

Therefore , the length of the new sign is 5.9 feet