Question

Find the value of h, if the distance between (h, 3) and (4, 5) is 5.

Answer 1

Given :

• AB distance is 5 Units.
• A( h , 3 )
• B( 4 , 5 )

Formula :

$\tt \dagger \: \: \: \: \: D = \sqrt{ {(x - x)}^{2} + {(y - y)}^{2} }$

Solution :

Let,

• A( h , 3 )
• B( 4 , 5 )

Now,

$\tt\mapsto AB = \sqrt{ {(4 - h)}^{2} + {(5 - 3)}^{2} }$

$\tt\mapsto 5 = \sqrt{16 + h - 8h + 4}$

$\tt\mapsto 5 = \sqrt{20 + {h}^{2} - 8h}$

$\tt\mapsto 5 = \sqrt{{h}^{2} -8h + 20}$

$\tt\mapsto 5 = \sqrt{ {h}^{2} -10h + 2h + 20}$

$\tt\mapsto 5 = \sqrt{h(h - 10) + 2(h - 10)}$

$\tt\mapsto 5 = \sqrt{(h - 10) (h + 2)}$

$\tt\mapsto 25 = (h - 10) (h + 2)$

$\rule{90}1$

Either,

$\tt\mapsto 25 = h - 10$

$\tt\mapsto h = 35.$

$\rule{90}1$

Or,

$\tt\mapsto h + 2 =25 .$

$\tt\mapsto h = 23.$

Therefore, the value of h is 23 and 35.