Question

In the following figure, EF || IH. LF and LI are right angles. If EF = 24 cm,
EI = 9 cm, FG = 7 cm and IH = 40 cm. Find the perimeter of the figure. ​

Answer 1

Given

• EF|| IH
• EI=9cm
• EF=24cm
• FG = 7cm
• IH= 40cm

To Find

• Find the perimeter of the figure.

Now in ∆ EFG

• EFG= 90⁰
• EF=24cm
• FG= 7 Cm

By Pythagorean Theorem

$\sf \: EG²= EF²+FG²$

$\sf \: EG²= 24²+7^{2}$

$\sf \: EG²= 576+49$

$\sf \: EG= \sqrt{625}$

• $\sf \: EG= 25 \: cm \: \: \: \: - - - (1)$

Now In ∆ EIH

• EIH= 90°
• EI= 9cm
• IH= 40cm

By Pythagorean Theorem

$\sf \: EH²= Ei²+Fh ^{2}$

$\sf \: EH²= 9²+40^{2}$

$\sf \: EH²= 81+1600$

$\sf \: EH= \sqrt{ 1681}$

• $\sf \: EH= 41cm \: \: \: \: - - - (2)$

On subtracting (1) From (2) We get,

GH= 41cm - 25cm

GH= 16 cm

Now In Figure EFGHI

• EI=9cm
• EF=24cm
• FG = 7cm
• IH= 40cm
• GH= 16 cm

$\sf \: perimeter \: of \: Figure \: = Sum \: Of \: All \: Side$

$\sf \: perimeter \: of \: Figure \: = 9 + 24 + 7 + 40 + 16cm$

• $\underline{\boxed {\sf \: perimeter \: of \: Figure \: = 96cm}}$

Answer 2

Step-by-step explanation:

Answer = (2) 96cm

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