Question

A parrallelogram PQRS has area 50cm^2

Given
- PQ has length 14cm
- QR has length 7cm
- angle SPQ is obtuse
find
(a) the size of angle SPQ in degrees, to 2 decimal place.

(b) the length of diagonal SQ, in cm to one decimal place.

Answer 1

SQ = 14.45 cm (sorry don't know the angle value)

Explanation:

To find the length of diagonal SQ, we can use the formula for the area of a parallelogram:

Area = base * height

In this case, we know that the area of PQRS is 50 cm^2. We can use the given lengths of PQ and QR as the base and height, respectively

Area = PQ * QR

50 = 14 * QR

To find QR, we can divide both sides of the equation by 14:

QR = 50/14 = 25/7 ≈ 3.57 cm

Now, to find the length of diagonal SQ, we can use the Pythagorean theorem. In a parallelogram, the diagonals bisect each other and create four right triangles.

Using the lengths PQ = 14 cm, QR = 3.57 cm, and angle SPQ = obtuse, we can find the length of diagonal SQ using the Pythagorean theorem:

SQ^2 = PQ^2 + QR^2

SQ^2 = 14^2 + (3.57)^2

SQ^2 ≈ 196 + 12.7449

SQ^2 ≈ 208.7449

SQ ≈ √208.7449 ≈ 14.45 cm