Question

Consider the enlargement of the pentagon. A small pentagon has a bottom side length of x centimeters and left side length of 7 centimeters. A larger pentagon has a bottom side length of 7 centimeters and left side length of 15 centimeters. Not drawn to scale What is the value of x, rounded to the nearest tenth? 2.1 centimeters 3.3 centimeters 7.0 centimeters 15.0 centimeters

Answer 1

The answer should be 3.3

Explanation:

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Answer 2

`x = 3.3cm`

Explanation:

Given

Shape: Pentagon

Small

`Bottom = x`

`Left = 7cm`

Big

`Bottom = 7cm`

`Left = 15cm`

Required

Find x

From the question, we understand that the big pentagon is a dilation of the small pentagon.

What this means is that; both pentagons will have the same equivalent ratio.

The equivalent ratio, in this case is calculated using

`Ratio = (Bottom)/(Left)`

For the small pentagon:

`Ratio = (x)/(7cm)`

For the big pentagon:

`Ratio = (7cm)/(15cm)`

Equate both ratios:

`(x)/(7cm) = (7cm)/(15cm)`

`(x)/(7cm) = (7)/(15)`

Cross multiply

`15 * x = 7cm * 7`

`15 * x = 49cm`

Make x the subject

`x = (49cm)/(15)`

`x = 3.267cm`

`x = 3.3cm` --- approximated