Question

this diagram shows right rectangular prism abcdefgh. it also shows $overline{eb}$ and $overline{hb}$. find the length of each diagonal shown in the diagram. if necessary, round your answers to the nearest tenth. $eb=square$ cm $hb=square$ cm

Explanation:

Step1: Find length of EB

In right - triangle ABE, by the Pythagorean theorem, in rectangle ABEF, $AE$ is the length, $AB$ is the width. First find the length of $EB$ in the base rectangle. Let $AE = 8$ cm and $AB=15$ cm. According to the Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}$, where $c = EB$, $a = 8$ and $b = 15$. So $EB=\sqrt{8^{2}+15^{2}}=\sqrt{64 + 225}=\sqrt{289}=17$ cm.

Step2: Find length of HB

In right - triangle EBH, we know $EB = 17$ cm and $EH=7$ cm. Using the Pythagorean theorem again, let $c = HB$, $a = 7$ and $b = 17$. Then $HB=\sqrt{7^{2}+17^{2}}=\sqrt{49+289}=\sqrt{338}\approx18.4$ cm.

Answer:

EB = 17 cm
HB = 18.4 cm