Question

3. In adjoining figure 1.14
seg PS 1. seg RO seg OT Log PR
IF RO - 6, PS = 6 and PR = 12
then find QT


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Answer 1

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Answer 2

Answer:

The length of QT is 3 units.

Step-by-step-explanation:

NOTE: Refer to the attachment for the diagram.

We have given that,

Seg PS ⊥ seg QT

Seg QT ⊥ seg PR

RQ = 6

PS = 6

PR = 12

We have to find QT.

We know that,

Area of triangle = ½ × base × height

A ( △ PQR ) = ½ × QR × PS

⇒ A ( △ PQR ) = ½ × 6 × 6

⇒ A ( △ PQR ) = 3 × 6

∴ A ( △ PQR ) = 18 sq. unit. - - ( 1 )

Now,

A ( △ PQR ) = ½ × PR × QT

⇒ 18 = ½ × 12 × QT - - [ From ( 1 ) ]

⇒ 18 = 6 × QT

⇒ QT = 18 ÷ 6

⇒ QT = 3 unit.

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Additional Information:

1. Area of triangle:

The place of occupied by the surface of a triangle is known as its area.

2. Formula for area of triangle:

Area of triangle = ½ × base × height

3. In acute angled triangle:

The height of the acute angled triangle is inside the triangle.

4. In obtuse angled triangle:

The height of the obtuse angled triangle is outside the triangle.

5. Triangle with two bases:

The area of triangle does not change although it's calculated with different bases.