the area of trapezium is 276cm2 and its height is 24cm.if one of its parallel side is longer than other by 7cm.find the length of parallel side.
shorter of parallel sides ---
longer of parallel sides --- x+7
(1/2)(x + x+7)(24) = 276
times 2
(2x+7)(24) = 552
divide by 24
2x+7 = 23
2x = 16
x = 8
parallel sides are 8 and 15
The area of a trapezium is 276 cm2 and it's height is 24cm if one of its parallel sides is longer than the other by 7cm find the length of parallel sides
To find the length of one of the parallel sides of the trapezium, we need to use the formula for the area of a trapezium.
The formula for the area of a trapezium is:
Area = (1/2) × (sum of parallel sides) × height
Given that the area of the trapezium is 276 cm^2, the height is 24 cm, and one of the parallel sides is longer than the other by 7 cm, let's denote the lengths of the parallel sides as a cm and (a + 7) cm.
Using the formula, we can write the equation as:
276 = (1/2) × (a + (a + 7)) × 24
Simplifying this equation, we get:
276 = (1/2) × (2a + 7) × 24
Now, we can solve for 'a':
Multiply both sides of the equation by 2 to eliminate the fraction:
2 × 276 = (2a + 7) × 24
552 = 48a + 168
Subtract 168 from both sides:
552 - 168 = 48a
384 = 48a
Divide both sides by 48:
384/48 = a
8 = a
Therefore, the length of one of the parallel sides of the trapezium is 8 cm.
The length of the other parallel side is (8 + 7) = 15 cm.
To find the length of the parallel side, we can use the formula for the area of a trapezium:
Area = (base1 + base2) * height / 2
Given that the area is 276 cm² and the height is 24 cm, we can substitute these values into the formula:
276 = (base1 + base2) * 24 / 2
To simplify the equation, we can divide both sides by 24:
11.5 = (base1 + base2) / 2
Next, we are given that one of the parallel sides is longer than the other by 7 cm. Let's assume the shorter side is x cm, then the longer side would be x + 7 cm.
Now, we can substitute these values into the equation:
11.5 = (x + x + 7) / 2
Multiply both sides by 2:
23 = 2x + 7
Subtract 7 from both sides:
16 = 2x
Finally, divide both sides by 2:
x = 8
So the length of the shorter side is 8 cm. The length of the longer side would be x + 7 = 8 + 7 = 15 cm.