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Points \( A \) and \( B \) are on the opposite edges of a pond as shown in the below figure. To find the distance between the two points, the surveyor makes a right-angled triangle as shown. Find the distance AB.
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Academic Mathematics NCERT Class 7

Given:

Points \( A \) and \( B \) are on the opposite edges of a pond as shown in the figure.

To find the distance between the two points, the surveyor makes a right-angled triangle as shown.
To do:

We have to find the distance AB.

Solution:

Let $AB=x$.

In the figure,

$AD=30\ m, DC=40\ m$
In right-angled triangle ADC,

$AD^2+DC^2=AC^2$

$(30)^2+(40)^2=(AB+BC)^2$

$900+1600=(x+12)^2$

$x^2+144+2(12)x=2500$

$x^2+24x+144-2500$

$x^2+24x-2356=0$

$x^2+62x-38x-2356=0$

$x(x+62)-38(x+62)=0$

$(x-38)(x+62)=0$

$x-38=0$ or $x+62=0$

$x=38$ or $x=-62$

$x=38$ (Distance cannot be negative)

Therefore, the distance between the points A and B is 38 m.

Updated on: 10-Oct-2022

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