Question

Quadrilateral ABCD is similar to Quadrilateral EFGH. Diagonal AC has length 7 and diagonal EG has length 13. What is the scale factor that describes a dilation from BC to FG? Give the exact scale factor and state whether the dilation is an expansion or a contraction.
If side AB has length 17/26 what is the length of side EF? Give the exact, un-rounded value.




PLEASE HELP ASAP

If the area of ABCD is 147 square inches, what is the area of EFGH? Give the exact answer.

Answer 1

Answer:

$\large \boxed{\text{A. }\dfrac{13}{7}\text{; B. }\dfrac{17}{14} \text{; C. 507 in}^{2}}$

Step-by-step explanation:

A. Scale factor

When you dilate an object by a scale factor, you multiply its line lengths by the same number.

If EF/AB = 13/7, the scale factor is 13/7.

B. Length of EF

$\begin{array}{rcl}\dfrac{EF}{AB} & = & \dfrac{13}{7}\\\\\dfrac{EF}{\frac{17}{26}} & = & \dfrac{13}{7}\\\\EF & = & \dfrac{13}{7}\times\dfrac{17}{26}\\\\ & = &\dfrac{1}{7}\times\dfrac{17}{2}\\\\ & = & \mathbf{\dfrac{17}{14}}\\\end{array}\\\text{The length of EF is \large \boxed{\mathbf{ \dfrac{17}{14}}} }$

C. Area of EFGH

If the lengths in a shape are all multiplied by a scale factor, then the areas will be multiplied by the scale factor squared.

ABCD is dilated by a scale factor of 13/7, so its area is dilated by a scale factor of

$\left(\dfrac{13}{7} \right)^{2} = \dfrac{169}{49}$

The area of its dilated image EFGH is

$\text{Area of EFGH} = \text{147 in}^{2} \times \dfrac{\text{169}}{\text{49}} = 3 \times 169\text{ in}^{2} = 507 \text{ in}^{2}\\\\\text{The area of EFGH is \large \boxed{\textbf{507 in}^{\mathbf{2}}} }$