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Question

a) gk2su

b) 14576u7ig

c) k3gfuigi79

d) 3y2efi3789i

Answer 1

Always know what the question is asking, draw a visual (which I have tried, but cannot seem to do in this platform) identify given information, then identify previously known information that might be helpful in establishing relationships needed to solve a problem.

A. the area of a rhombus is given as 75cm²

B. The length of a diagonal BD is (2/3)the length of AC, so (3/2) the length of BD is the length of AC

C. Since a rhombus

1. All sides are equal
2. Each diagonal, by itself, cuts the rhombus' area in half, so that the area of the rhombus is twice the area of any one triangle created by a diagonal and two sides.
3. Each diagonal is a perpendicular bisector of the other diagonal
4. The area of a triangle is (1/2)bh, so that (from above) the area of the rhombus is 2((1/2)(bh)=bh. where b is the length of one diagonal and h is the length of 1/2 the other diagonal.
5. We also know the area of a rhombus is the product of the length of any one side with the shortest distance to the opposing side.
6. We also know the Pythagorean theorem applies to right triangles.

From the above information and our illustration, we figure out what strategies we might apply. If we start out with the last two pieces of information, we my become discouraged, so we try using the 2nd 3rd and 4th pieces of information about a rhombus.

From 4. we can write

(length of BD)(1/2)(length of AC) = 75cm²

NOTE: This means that (1/2)(length of BD)(length of AC)= (the area of any rhombus).

or more generally,

The area of a rhombus is the product of the length of its diagonals.

So, in our case, (1/2)(length of BD)(length of AC)=75

From B, the length of AC is 3/2 the length of BD

So,

(1/2)[(length of BD)][(3/2)(length of BD)]=75

(1/2)(3/2)(length of BD)(length of BD)=75

(3/4)(length of BD)²=75

(length of BD)²=(4/3)75

(length of BD)²=100

The length of BD is 10cm.

Answer 2

Given Area = 225 cm²

Given Diagonal AC and BD=(2/3)AC

Area of a rhombus = product of their diagonals / 2. Area = ACx(2/3)AC = (2/3)AC²

Then (2/3)AC² = 225

AC² = 225x3/2 = 225

AC = √225

AC = 15 cm or answer D)