Question

SOLVE THIS.

#DONT SPAM. ​

Answer 1

SOLUTION :-

➠ Understand and explore the problem

➠ We have to find the values of x, y, z.

i.e. OE, OY and side IR of the rhombus

and perimeter of the rhombus.

➠What do we know?

RICE is a rhombus and

OC = 12, OE = 5, OI = x + 2, OR = x + y.

➠Plan a strategy

(1) We have to find the parts of the diagonal. Use diagonals of a rhombus bisect each other.

(2) We have to find the side of the rhombus. We use diagonals intersect at right angles and apply pythagoras theorem.

(3) Since all sides of a rhombus are equal, perimeter of the rhombus = 4 × side.

➠Solve

➠step (1) . OI = OE ⇒ x + 2 = 5 or x = 5 – 2 = 3.

OC = OR ⇒ 12 = y + x or y = 12 – x

12 – 3 = 9

➠step(2):- EOR is a right triangle

➠ER² = OE² + OR²

➠ER² = 5² + 12²

➠ER² = 25 + 144 = 169.

➠.°. ER = 13cm.

➠step (3) :- Since all sides of a rhombus are equal.

➠∴ RE = RI = IC = CE = 13 cm.

➠Perimeter of RICE = 4 × RE = 4 × 13 cm

= 52 cm

Revise

➠We have been asked to find x, y and z and we have found

that.

Checking

➠x + 2 = 5 and x = 3 ⇒ 3 + 2 = 5

➠Hence value of x is correct.

➠x + y = 12  x = 3 and y = 9

➠and 3 + 9 = 12 ⇒ value of y is correct.

➠Perimeter of rhombus = 2 √( d1)²+ (d2)² (where d1 and d2 are diagonals)

= 2 √24² + 10²

= 2 √576+ 100

= 2 √676 = 52 cm.

hence, the perimeter of the rhombus is 52cm.