a plant 90cm high broke at a point but did not separate its top touches the ground of 27cm from its base find the height of the point from the ground at which the plant broke
hard
To find the height of the point from the ground at which the plant broke, we can use the concept of similar triangles.
Let's denote the height of the point from the ground at which the plant broke as 'x'.
We have two similar triangles: the larger triangle formed by the entire height of the plant (90 cm) and the distance from the base to the top (27 cm), and the smaller triangle formed by the broken part of the plant and the distance from the break point to the top (x cm).
Using the concept of similar triangles, we can set up a proportion:
(27 cm) / (90 cm) = (x cm) / (60 cm)
To solve for 'x', we can cross-multiply and then solve the equation:
27 cm * 60 cm = 90 cm * x cm
1620 cm² = 90 cm * x cm
Now, we can solve for 'x' by dividing both sides of the equation by 90 cm:
1620 cm² / 90 cm = x cm
18 cm = x
Therefore, the height of the point from the ground at which the plant broke is 18 cm.
To find the height of the point where the plant broke, we can use the concept of similar triangles.
Let's assume that the height of the broken part of the plant is h cm. Since the top of the plant touches the ground at a distance of 27 cm from its base, the remaining part (unbroken) of the plant would be 90 cm - 27 cm = 63 cm.
Now, we have two similar triangles:
1. The entire plant (90 cm) and the unbroken part of the plant (63 cm).
2. The unbroken part of the plant (63 cm) and the broken part (h cm).
The ratio of the corresponding sides of two similar triangles is equal. Therefore, we can set up the following proportion:
90 cm / 63 cm = 63 cm / h cm
To solve for h, we can cross multiply and then divide:
90 cm * h cm = 63 cm * 63 cm
h cm = (63 cm * 63 cm) / 90 cm
Now, let's calculate the value of h:
h cm = (63 cm * 63 cm) / 90 cm
h cm ≈ 44.1 cm
Therefore, the height of the point where the plant broke from the ground is approximately 44.1 cm.
if the height is x,
x^2 + 27^2 = (90-x)^2
x = 40.95