Question

The quadrilateral-shaped field has an area of 650 m². If the altitudes
measure 6.6 m and 6.4 m respectively, then find the length of the
diagonal of the field.
​

Answer 1

Step-by-step explanation:

The quadrilateral-shaped field has an area of 650 m². If the altitudes

measure 6.6 m and 6.4 m respectively, then find the length of the

diagonal of the field.

Answer 2

$\huge{\green{\underline{\underline{Answer:-}}}}$

Given:

Quadrilateral shaped field has an area of 650 m². Altitude measure 6.6m and 6.4m

To find:

Length of diagonal of the field = ?

Solution:

Refer attachment for figure

In quadrilateral PQRS, QS is the diagonal and PT, UR is the altitude of triangle QPS and QRS

Let x be the length of diagonal

Area of Quadrilateral PQRS = Area of ΔQPS + Area of Δ QRS

$\\ \\ Area \: of \: quadrilateral \: = \\ \\ \dfrac{1}{2} \times Base \: QS × Height \: PT + \\ \dfrac{1}{2} \times Base \: QS × Height \: RU$

$\\ \\ 650 = \dfrac{1}{2} \times x ×6.6 + \\ \dfrac{1}{2} \times x×6.4 \\ \\ 650 = 3.3x + 3.2x \\ \\ 650 = 6.5x$

$\\ \\ \dfrac{650}{6.5} = x \\ \\ \dfrac{6500}{65} = x \\ \\ 100 = x \\ \\ length \: of \: diagonal \: is \: 100 \: m$

Required answer:

Thus, length of diagonal of the field is 100 m

Knowledge booster:

• Area of triangle = 1/2 × base × height
• Altitude of triangle is perpendicular line drawn from vertex of triangle to opposite side
• Solve more such questions to get good hold on it