The longer base of an isosceles trapezium is 20 cm, its legs are 10cm. The legs of the trapezium are extended by 8 cm long to gain an isosceles triangle.Find the shorter base of the trapezium. Please help me:)
did you make a sketch?
I have a large isosceles triangle containing your original trapezium
The sides of the triangle are made up of the segments 10 and 8 for a total length of 18 each
I see a smaller isosceles triangle contained and similar to a larger isosceles triangle
let the smaller base be x
remember the sides of similar triangles are in the same ratio
so....
x/8 = 20/18
x = 8(20/18) = 80/9 or appr. 8.89 cm
thank u so much!:)
To find the shorter base of the trapezium, we can start by understanding the given information and using some geometry principles.
Let's denote the shorter base of the trapezium as "x cm".
From the question, we know that the longer base of the trapezium is 20 cm and the legs are 10 cm each. Additionally, we are told that the legs of the trapezium are extended by 8 cm each to form an isosceles triangle.
To find the shorter base, we can apply the following steps:
Step 1: Calculate the lengths of the extended legs of the trapezium.
Since the legs of the trapezium are extended by 8 cm each, the new lengths of the legs can be calculated as:
length of extended legs = length of original legs + extension
= 10 cm + 8 cm
= 18 cm
Step 2: Calculate the height of the isosceles triangle.
The height of an isosceles triangle can be found by applying the Pythagorean Theorem. Since the length of the shorter base (x cm) divides the triangle into two congruent right triangles, the height can be calculated as:
height = √[(length of extended legs)² - (length of original legs)²]
= √[(18 cm)² - (10 cm)²]
= √[324 cm² - 100 cm²]
= √224 cm²
= 14.97 cm (rounded to two decimal places)
Step 3: Use the height and the given lengths to set up an equation to solve for the shorter base.
In an isosceles trapezium, the height is the perpendicular distance between the parallel bases. We can use this information to set up the following equation:
x = (length of longer base - length of shorter base) / 2 + 2 * (height)
Substituting the given values into the equation:
x = (20 cm - x cm) / 2 + 2 * (14.97 cm)
2x = 20 cm - x cm + 29.94 cm
3x = 49.94 cm
x ≈ 16.65 cm (rounded to two decimal places)
Therefore, the shorter base of the trapezium is approximately 16.65 cm.