A 34.56 cm2 rectangle was cut from the rectangle of the plate with sides 7.4

| June 1, 2021 | education

A 34.56 cm2 rectangle was cut from the rectangle of the plate with sides 7.4 cm and 6.4 cm. Find the lengths of the sides of the remaining part of the plate

ABCD – rectangular plate, in which AB = CD = 6.4 cm; AD = BC = 7.4 cm.

OMCD (shaded) – the part that was cut off. S ОМСD = 34.56 cm2.

You need to find: the lengths of the sides BM, AO, AB and OM.

1) The length AB is known by condition (it is equal to 6.4 cm). And the OM side is equal to the AB side, that is, OM = 6.4 cm.

2) Find the area of ​​the entire plate:

7.4 x 6.4 = 47.36 (cm2).

2) Find the area of ​​the part that remained after the OMCD part was cut off. This is part of ABMO.

47.36 – 34.56 = 12.8 (cm2).

3) Consider a rectangle ABMO. We know its area and sides AB, OM. The sides BM and AO are equal. They can be found using the formula for calculating the area of ​​a rectangle (S = ax in), from which we express a (a = S: b):

12.8: 6.4 = 2 (cm).

Answer: the sides of the remaining part of the plate have the following dimensions: BM = AO = 2 cm; AB = OM = 6.4 cm.



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