Question

Vishal bought a photo frame in the shape of a
parallelogram. If the base and height of he
photo fraine are in the ratio 2:3 and arca
covered by the frame is 864 cm2. Then, find the
length of the base of the photo frame. a) 46cm b) 24cm c 34 d) 36
​

Answer 1

{Some corrections in the question}

Question : Vishal bought a photo frame in the shape of a parallelogram. If the base and height of the photo frame are in the ratio 2:3 and area covered by the frame is 864 cm². Then, find the length of the base of the photo frame.

Solution : According to the question, the base and height of the photo frame are in the ratio 2:3.

Let, the base and height of the photo frame be 2x and 3x respectively.

Hence,

➜ Base of photo frame = 2x ----{1}

➜ Height of photo frame = 3x ----{2}

Also we know that, the area of the photo frame is 864 cm².

Now, by formula : Area of parallelogram

➜ Area of photo frame = base * height

➜ 864 = 2x * 3x

➜ 864 = 6x² i.e.

➜ 6x² = 864

➜ x² = 864/6

➜ x² = 144

➜ x = √144

➜ x = 12 cm

Now, put value of x in {1} and {2}

➜ Base of photo frame = 2x

➜ Base of photo frame = 2 * 12

➜ Base of photo frame = 24 cm and

➜ Height of photo frame = 3x

➜ Height of photo frame = 3 * 12

➜ Height of photo frame = 36 cm

Answer : Hence, the length of the base of the photo frame is 24 cm. [Answer : b) 24 cm].