Question

The diagram of PQR below shows the lengths of two sides and an altitude.

A
19 units

B
21 units

C
27 units

D
35 units

Answer 1

B) Length of PR is 21 unit.

Explanation:

In Δ PQR, PQ = 10 unit , and QR = 17 unit (given)

and let, QT⊥ PR.

Now, QT = 8 unit (given)

So, Δ PQT is a right angled triangle right-angled at T .

So. PT =
`\sqrt {((PQ)^(2) - (QT)^(2))}`

=
`\sqrt {10^(2) - 8^(2)}`

=
`√(36)` = 6 unit

Similarly,

Δ RQT is a right angled triangle right-angled at T .

So. RT =
`\sqrt {((RQ)^(2) - (QT)^(2))}`

=
`\sqrt {17^(2) - 8^(2)}`

=
`√(225)` = 15 unit

So, PR = PT + TR = (15 + 6) unit = 21 unit