Question

Two vertical poles of height 9 m and 14 m stand on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Distance\:between\:their\:tops=13\:m}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Fiven :}} \\ \tt: \implies Length \: AD = 9 \: m \\ \\ \tt: \implies Length \: EC = 14 \: m \\ \\ \tt: \implies Length \: DC=12 \: m \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Length \: AE = ?$

• According to given question :

$\tt \circ \:DC= AB = 12 \: m \\ \\ \tt \circ \: AD= BC = 9 \: m\\ \\ \tt : \implies EB = EC - BC \\ \\ \tt: \implies EB = 14 - 9 \\ \\ \tt \circ \: EB = 5 \: m \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies {h}^{2} = {p}^{2} + {b}^{2} \\ \\ \tt: \implies {AE}^{2} = {AB}^{2} + {EB}^{2}\:\:\:\:\:(By\:phythagoras\:theorem) \\ \\ \tt: \implies {AE}^{2} = {12}^{2} + {5}^{2} \\ \\ \tt: \implies {AE}^{2} =144 + 25 \\ \\ \tt: \implies {AE}^{2} =169 \\ \\ \tt: \implies {AE} = \sqrt{169} \\ \\ \green{\tt: \implies {AE} =13 \: m} \\ \\ \green{\tt\therefore Distance \: between \: their \: tops \: is \: 13 \: m}$

Answer 2

ANSWER

13m

CONCEPT USED

• PYTHAGOURES THEOREM
• PROPERTY OF RECTANGLE

EXPLANATION

GIVEN

AB = 12m, AD=9m, BC=12m

DC = ?

BY PROPERTY OF RECTANGLE

AB= DE = 12 m AND AND AD = BE = 9m

{AS DE PARALLEL TO AB AND AD PARALLEL TO BE

AND ANGLE A AND B ARE 90 SO IT IS A RECTANGLE}

BC = 14m = BE + EC= 9+EC

which implies

EC = 5m

Apply pythagoures theorem in ∆CED

DC = √ DE^2+EC^2

=√ 12 ^2 + 5^2

=√169

= 13m

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