Question

How do I solve for the missing lengths?

Answer 1

Answer:

Part 4) $ER=3\ units$

Part 5) $DF=9\sqrt{10}\ units$

Part 6) $DE=30\ units$

Step-by-step explanation:

Part 4) Find ER

we know that

In the right triangle ERF

Applying the Pythagorean Theorem

$EF^2=ER^2+RF^2$

substitute the given values

$(3\sqrt{10})^2=ER^2+9^2$

solve for ER

$ER^2=(3\sqrt{10})^2-9^2$

$ER^2=90-81\\ER^2=9\\ER=3\ units$

Part 5) Find DF

we know that

In the right triangle DRF

Applying the Pythagorean Theorem

$DF^2=DR^2+RF^2$

substitute the given values

$DF^2=27^2+9^2$

$DF^2=810\\DF=\sqrt{810}\ units$

simplify

$DF=9\sqrt{10}\ units$

Part 6) Find DE

we know that

$DE=DR+RE$ ----> by segment addition postulate

we have

$DR=27\ units\\RE=ER=3\ units$

substitute

$DE=27+3=30\ units$